Under what condition do langle (1/√2) , (1/2) , k rangle represent direction cosines of a line?

Question

Under what condition do langle (1/√2) , (1/2) , k rangle represent direction cosines of a line? (A)  k = (1/2) (B)  k = - (1/2) (C)  k = ± (1/2) (D) k can take any value

Tardigrade Admin · Accepted Answer

For ((1/√2) , (1/2),k) to represent direction cosines ((1/√2))2 + ((1/2))2 + k2 = 1 or , (1/2) + (1/4) + k2 = 1 (3/4) + k2 = 1⇒ k = ± (1/2)

Q. Under what condition do $⟨ \frac{1}{2}, \frac{1}{2}, k ⟩$ represent direction cosines of a line?

$k = \frac{1}{2}$

$k = - \frac{1}{2}$

$k = \pm \frac{1}{2}$

k can take any value

For $(\frac{1}{2}, \frac{1}{2}, k)$ to represent direction cosines
$(\frac{1}{2})^{2} + (\frac{1}{2})^{2} + k^{2} = 1$
or , $\frac{1}{2} + \frac{1}{4} + k^{2} = 1$
$\frac{3}{4} + k^{2} = 1 \Rightarrow k = \pm \frac{1}{2}$

Q. Under what condition do ⟨2​1​,21​,k⟩ represent direction cosines of a line?

k=21​

k=−21​

k=±21​